Independent computational reproduction

Verdicts: {"C1": "reproduced", "C2": "reproduced", "C3": "reproduced", "C4": "reproduced", "C5": "reproduced"}. All 14 evidence-result comparisons match the declared values within their tolerances. Both complete result objects also match the declared object: True.

The supplied code was read and rerun in Python 3.12.15 with an initially empty output directory. Its declared output was not mounted into the computation. A separately written verifier enumerated all primes through the stated limit using a segmented sieve over all integers, rather than the supplied global odd-number sieve. It independently accumulated each residue-class race over the intervals between primes. Every event interval was inclusive at both endpoints, and the initial interval and final tail were counted. The prime 2 was explicitly included in the modulo-three class, and prime 3 was excluded from both classes modulo three.

For a prefix through 30,000, the independent segmented sieve exactly agreed with trial division for every prime. The interval-based counts and race durations also matched a separate direct scan of every integer in that prefix, covering the first reversal and guarding against endpoint mistakes. The complete duration counts partition the stated integer range exactly for each race.

For the weighted share, the independent verifier directly summed 1/x over every integer in the leading intervals with mpmath 1.3.0 at 50 decimal digits and used mpmath.harmonic for the denominator. It did not use the supplied Euler-Maclaurin harmonic approximation or endpoint subtraction. The unrounded high-precision numerator, denominator, and ratio are attached in independent-audit.json; the rounded results match the declared outputs within tolerance.

The supplied run completed in 5.419 seconds and the independent run in 6.178 seconds, together within the declared two-minute budget. Both containers had no network, read-only root filesystems, no capabilities or privilege escalation, an unprivileged numeric user, and CPU, memory, process, and time limits. Only the required code and an initially empty result directory were mounted. The independent verifier read neither supplied code nor declared result values.

Integrity and caveats: all nine supplied files were read. The node reported no orphan numbers, missing sections or files, data anomalies, or skipped tables. The text scan found no hidden Unicode controls, formatting, surrogate, or private-use characters, and the paper contains no raw HTML or instructions directed at verifiers. One source comment says prime 2 is in neither race's classes; it actually belongs to the winning class modulo three. The executed step function and independent verifier handle this correctly, so the comment error does not affect the computational verdicts.

Scope: these verdicts reproduce finite counts and the finite weighted share. They do not establish the conditional limiting-density results cited in the paper or resolve their hypotheses. Those require separate citation and domain review.

Hazard screen: none. This is a deterministic mathematical enumeration of primes with harmless numerical calculations and no personal or field data.